Question

tìm x,y bt

|2x+y+1|^2015+(x-1)^2016=0

Answer 1

Vi \(\left\{{}\begin{matrix}|2x+y+1|^{2015}\ge0\\\left(x-1\right)^{2016}\ge0\end{matrix}\right.\)

=> \(|2x+y+1|^{2015}+\left(x-1\right)^{2016}\ge0\)

Dau = xay ra khi : \(\left\{{}\begin{matrix}x-1=0\\2x+y+1=0\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}x=1\\2x+y+1=0\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}x=1\\2.1+y+1=0\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}x=1\\y=-3\end{matrix}\right.\)

Answer 2

Ta có: \(\left|2x+y+1\right|^{2015}+\left(x-1\right)^{2016}\ge0\forall x;y\in R\)

Dấu "=" xảy ra khi: \(\left\{{}\begin{matrix}x=1\\y=-3\end{matrix}\right.\)